66
CHAPTER 3, FORM A
COLLEGE ALGEBRA
NAME
DATE
1. Sketch the graph of the quadratic function
( )
2
3 6 5.f x x x= − − −
Give the intercepts, the
vertex, the axis, the domain, and the range.
1.
x-intercepts: _________________________
y-intercepts: _________________________
vertex: _____________________________
axis: _______________________________
domain: ____________________________
range: ______________________________
2. A rock is propelled upward from the top of a building 2. _______________________________
60 feet tall at an initial velocity of 40 feet per second. The
function that describes the height of the rock in terms of
time t is
( )
2
16 40 60.f t t t= + +
Determine the maximum
height that the rock reaches.
Use synthetic division to perform each division.
3.
5 4 3 2
4 20 14 14 12
1
x x x x x
x
− + − + +
−
3. q(x): ___________________________
r: ______________________________
4.
42
5 14
4
x x x
x
+−
+
4. q(x): ___________________________
r: ______________________________
5. Use synthetic division to determine
( )
3,f
if 5. ________________________________
( )
5 3 2
3 4 5 2.f x x x x= − − +
67
CHAPTER 3, FORM A
6. Use the factor theorem to determine whether the polynomial 6. ________________________________
2x−
is a factor of
5 2 3
3 4 5 8 25.x x x x− − − +
If it is, what is the other factor? ________________________________
If it is not, explain why.
7. Find all zeros of
( )
,fx
given that 7. ________________________________
( )
32
88f x x x x= − − +
and 1 is one zero.
8.
( )
fx
is a third degree polynomial having only real 8. ________________________________
coefficients. It has 5 and
i−
as zeros, and the point
()
2,105−
lies on the graph. Find
( )
fx
.
9. Consider the function defined by
( )
32
2 3 5 4.f x x x x= − − + +
a. Use the intermediate value theorem to show that f has a 9. a. _______________________________
zero between 0 and
1.−
b. Use a graphing calculator to final all real zeros to as b. _______________________________
10. Explain why the polynomial function defined by 10. ________________________________
( )
62
2 4 8f x x x= + +
cannot have any real zeros.
many decimal places as the calculator will give.
11. Graph the functions defined by
( )
4
1
f x x=
and
( ) ( )
4
2112
2
f x x= − − +
on the same axes. Explain
how the graph of
2
f
can be obtained by a
translation of the graph of
1.f
11.
________________________________
________________________________
68
CHAPTER 3, FORM A
12. Use end behavior to determine which of the following graphs 12. _______________________________
is that of
( )
92
2 3.f x x x= − +
a. b.
c. d.
Graph each polynomial function. Factor first if the expression is not in factored form.
13.
( ) ( ) ( ) ( )
1 2 4f x x x x= + − −
13. _______________________________
14.
( ) ( ) ( ) ( )
2
1 3 2f x x x x= − − +
14. _______________________________
15.
( )
432
22f x x x x= − + −
15. _______________________________
16. Find a cubic polynomial having the graph shown. 16. _______________________________
17. Based on information provided by the U.S. Institute on 17. _______________________________
Drug Abuse, the percent y of 18- to 25-year-olds who had
used hallucinogens between 1974 and 1991 can be modeled
by the function
32
.025 .7 4.43 16.77,y x x x= − + +
where
0x=
corresponds to the year 1974. In what year during this
period did this type of drug use each its minimum?
69
CHAPTER 3, FORM A
18.
( )
3
1
fx x
=+
18.
19.
( )
2
2
2
4
x
fx x
+
=−
19.
70
CHAPTER 3, FORM A
20. For the rational function defined by
( )
24,
x
fx x
−
=
a. determine the equation of the oblique asymptote; 20. a. _____________________________
b. determine the x-intercepts; b. ____________________________
c. determine the y-intercepts; c. ____________________________
d. determine the equation of the vertical asymptote; d. ____________________________
e. sketch the graph. e.
21. The pressure of a gas varies jointly as its density and its 21. _______________________________
absolute temperature. When the density of a gas is
.75 g per cubic liter and the absolute temperature is
400 ,
the pressure is 20 newtons per sq m. Find the pressure per
cubic liter when the density is 4.00 g per cubic liter and
the absolute temperature is
60 .
22. The illumination (in foot-candles) of a light source varies 22. _______________________________
directly as the intensity (in candle-power) of the source and
inversely as the square of the distance from the source. If
a certain light source with intensity of 300 candle-power
provides an illumination of 2.5 foot-candles at a distance
of 40 ft, what is the illumination at a distance of 20 ft?
71
CHAPTER 3, FORM B
COLLEGE ALGEBRA
NAME
DATE
1. Sketch the graph of the quadratic function
( )
2
3 6 1.f x x x= − − −
Give the intercepts, the
vertex, the axis, the domain, and the range.
1.
x-intercepts: _________________________
y-intercepts: _________________________
vertex: _____________________________
axis: _______________________________
domain: ____________________________
range: ______________________________
2. Joe owns a hotdog stand. He has found that his
profit can be approximated by the model
( )
260 76,P x x x= − + +
where P is the profit
(in dollars) and x is the number of hotdogs sold.
a. Based on this model, what is his profit if he 2. a. _______________________________
sells 45 hotdogs?
b. Find the number of hotdogs he must sell to b. _______________________________
earn the maximum profit. What is the maximum
profit?
Use synthetic division to perform each division.
3.
43
4 3 5
3
x x x
x
− − +
−
3. q(x): ___________________________
r: ______________________________
4.
4 3 2
4 15 19 6
6
x x x x
x
− − + −
−
4. q(x): ___________________________
r: ______________________________
5. Use synthetic division to determine
( )
3,f
if 5. ________________________________
( )
32
3 5.f x x x= − − +
72
CHAPTER 3, FORM B
6. Use the factor theorem to determine whether the polynomial 6. ________________________________
3x+
is a factor of
5 4 3 2
2 3 10 6 18.x x x x x+ − + + −
If it is, what is the other factor? ________________________________
If it is not, explain why.
7. Find all zeros of
( )
,fx
given that 7. ________________________________
( )
32
3 10 24f x x x x= + − −
and 3 is one zero.
8.
( )
fx
is a fourth degree polynomial having only real 8. ________________________________
coefficients. It has
4, ,i−−
and 2 as zeros, and the
point
()
3,50−
lies on the graph. Find
( )
fx
.
9. Consider the function defined by
( )
32
2 5 4.f x x x x= − − +
a. Use the intermediate value theorem to show that f has a 9. a. _______________________________
zero between
1−
and
2.−
b. Use a graphing calculator to final all real zeros to as b. _______________________________
many decimal places as the calculator will give.
10. Explain why the polynomial function defined by 10. ________________________________
( )
62
5 7 2f x x x= − − −
cannot have any positive
real zeros.
11. Graph the functions defined by
( )
3
1
f x x=
and
( ) ( )
3
22 3 2f x x= − − +
on the same axes. Explain how
the graph of
2
f
can be obtained by a translation of the
graph of
1.f
11.
________________________________
________________________________
73
CHAPTER 3, FORM B
12. Use end behavior to determine which of the following graphs 12. _______________________________
is that of
( )
73
3 5.f x x x= + +
a. b.
c. d.
Graph each polynomial function. Factor first if the expression is not in factored form.
13.
( )
5 4 3
121
3 3 3
f x x x x= − +
13. _______________________________
14.
( ) ( ) ( ) ( ) ( )
1 1 2 3f x x x x x= + − + +
14. _______________________________
15.
( ) ( ) ( ) ( )
3 2 2f x x x x x= − + −
15. _______________________________
16. Find a cubic polynomial having the graph shown. 16. _______________________________
17. Based on information provided by the U.S. Institute on 17. _______________________________
Drug Abuse, the percent y of 18- to 25-year-olds who had
used hallucinogens between 1974 and 1991 can be modeled
by the function
32
.025 .7 4.43 16.77,y x x x= − + +
where
0x=
corresponds to the year 1974. In what year during this
period did this type of drug use each its minimum? (Round
to the nearest whole year.)
74
CHAPTER 3, FORM B
18.
( )
2
2
16
4
x
fx x
−
=−
18.
19.
( )
2
6
4
fx x
=+
19.
75
CHAPTER 3, FORM B
20. For the rational function defined by
( )
29,
4
x
fx x
−
=+
a. determine the equation of the oblique asymptote; 20. a. _____________________________
b. determine the x-intercepts; b. ____________________________
c. determine the y-intercepts; c. ____________________________
d. determine the equation of the vertical asymptote; d. ____________________________
e. sketch the graph. e.
21. The electrical resistance of a wire varies directly 21. _______________________________
as its length and inversely as the as the square of its
diameter. If the resistance of 640 ft of copper
wire
1
4
in. in diameter is 16 ohms, find the
resistance of 320 ft of the same type of copper
wire
1
2
in. in diameter.
22. Hooke’s Law for an elastic spring states that the 22. _______________________________
distance a spring stretches varies directly as the
force is applied. If a force of 25 pounds stretches
a certain spring 7 inches, then how much will a
force of 100 pounds stretch the spring?
76
CHAPTER 3, FORM C
COLLEGE ALGEBRA
NAME
DATE
1. Sketch the graph of the quadratic function
( )
2
14 6.
2
f x x x= − − −
Give the intercepts, the
vertex, the axis, the domain, and the range.
1.
x-intercepts: _________________________
y-intercepts: _________________________
vertex: _____________________________
axis: _______________________________
domain: ____________________________
range: ______________________________
2. Melissa sells umbrellas. She finds that her profit can
be approximated by the model
( )
2
2 92 110,P x x x= − + +
where P is the profit in dollars and x is the number
of batons sold.
a. Based on this model, what is her profit if she 2. a. _______________________________
sells 40 umbrellas?
b. Find the number of umbrellas she must sell to b. _______________________________
earn the maximum profit. What is the maximum
profit?
Use synthetic division to perform each division.
3.
32
5 10 8 10
1
x x x
x
− + +
+
3. q(x): ___________________________
r: ______________________________
4.
51
1
x
x
−
−
4. q(x): ___________________________
r: ______________________________
5. Use synthetic division to determine
( )
3,f−
if 5. ________________________________
( )
4 3 2
8 14 8 15.f x x x x x= − + + −
77
CHAPTER 3, FORM C
6. Use the factor theorem to determine whether the polynomial 6. ________________________________
2x+
is a factor of
42
4 3 2 5 8.x x x x− + − +
If it is, what is the other factor?
If it is not, explain why.
7. Find all zeros of
( )
,fx
given that 7. ________________________________
( )
32
4 12 3f x x x x= − − +
and 3 is one zero.
8.
( )
fx
is a fourth degree polynomial having only real 8. ________________________________
coefficients. It has
3, 4,and i−−
as zeros, and the
point
()
3, 120−−
lies on the graph. Find
( )
fx
.
9. Consider the function defined by
( )
32
2 5 7 1.f x x x x= + − +
a. Use the intermediate value theorem to show that f has a 9. a. _______________________________
zero between
3−
and
4.−
b. Use a graphing calculator to final all real zeros to as b. _______________________________
many decimal places as the calculator will give.
10. Explain why the polynomial function defined by 10. ________________________________
( )
42
4f x x x=+
has only one real zero.
11. Graph the functions defined by
( )
4
1
f x x=
and
( ) ( )
4
2121
2
f x x= + −
on the same axes. Explain how
the graph of
2
f
can be obtained by a translation of the
graph of
1.f
11.
________________________________
________________________________
78
CHAPTER 3, FORM C
12. Use end behavior to determine which of the following graphs 12. _______________________________
is that of
( )
63
3 5.f x x x= − +
a. b.
c. d.
Graph each polynomial function. Factor first if the expression is not in factored form.
13.
( ) ( ) ( ) ( )
2 1 4f x x x x x= + − +
13. _______________________________
14.
( ) ( ) ( ) ( )
2
3 1 2f x x x x= + + −
14. _______________________________
15.
( )
432
3 12 12f x x x x= + +
15. _______________________________
16. Find a cubic polynomial having the graph shown. 16. _______________________________
17. A technique for measuring cardiac output depends 17. _______________________________
on the concentration of a dye in the bloodstream
after a known amount is injected into a vein near
the heart. For a normal heart, the concentration of
dye in the bloodstream at the time x (in seconds) is
modeled by the function
( )
4 3 2
.006 .140 .053 1.79 .g x x x x x= − + − +
According to this model, how long after the injection
does the concentration reach its maximum? (Round
to the nearest tenth of a second.)
79
CHAPTER 3, FORM C
18.
( )
3
2
fx x
=−
18.
19.
( )
42
2
x
fx x
−
=+
19.
80
CHAPTER 3, FORM C
20. For the rational function defined by
( )
228
,
3
xx
fx x
+−
=+
a. determine the equation of the oblique asymptote; 20. a. _____________________________
b. determine the x-intercepts; b. ____________________________
c. determine the y-intercept; c. ____________________________
d. determine the equation of the vertical asymptote; d. ____________________________
e. sketch the graph. e.
21. The weight of a liquid varies directly as its 21. _______________________________
volume V. If the weight of the liquid into a cubical
container 4 cm on a side Is 192 g, find the weight
of the liquid in a cubical container 5 cm on a side.
22. The elongation in a wire when a mass is hung 22. _______________________________
at its free end varies jointly as the mass and
the length of the wire and inversely as the
cross-sectional area of the wire. The elongation
is .0072 cm when a mass of 160 gm is attached
to a wire 330 cm long, with a cross-sectional area
of .4 sq cm. Find the elongation if a mass of 120 gm
is attached to the same wire.
81
CHAPTER 3, FORM D
COLLEGE ALGEBRA
NAME
DATE
1. Sketch the graph of the quadratic function
( )
2
14 16.
3
f x x x= − +
Give the intercepts, the
vertex, the axis, the domain, and the range.
1.
x-intercepts: _________________________
y-intercepts: _________________________
vertex: _____________________________
axis: _______________________________
domain: ____________________________
range: ______________________________
2. If a model rocket is fired upward from ground
level, its position s (in feet) above the ground at
any time t (in seconds) is given by the function
( )
2
160 16 .s t t t=−
a. Find the height of the rocket 3 sec after 2. a. _______________________________
it is fired.
b. Find the maximum height of the rocket b. _______________________________
and the time it takes the rocket to reach
that height.
Use synthetic division to perform each division.
3.
43
3 8 10 3
2
x x x
x
− + +
−
3. q(x): ___________________________
r: ______________________________
4.
2
5 13 10
2
x x x
x
− − − +
+
4. q(x): ___________________________
r: ______________________________
5. Use synthetic division to determine
( )
2,f
if 5. ________________________________
( )
6 5 4 3 2
3 2 3 2 5 5.f x x x x x x x= + + + − + +
82
CHAPTER 3, FORM D
6. Use the factor theorem to determine whether the polynomial 6. ________________________________
4x−
is a factor of
4 3 2
2 13 24 16.x x x x− − + −
If it is, what is the other factor? ________________________________
If it is not, explain why.
7. Find all zeros of
( )
,fx
given that 7. ________________________________
( )
( )
2
213 36f x x x= + +
8.
( )
fx
is a third degree polynomial having only real 8. ________________________________
coefficients. It has 1, 3 and
4−
as zeros, and the
point
()
2,30−
lies on the graph. Find
( )
fx
.
9. Consider the function defined by
( )
32
4 5 6.f x x x x= − + + −
a. Use the intermediate value theorem to show that f has a 9. a. _______________________________
zero between 4 and 5.
b. Use a graphing calculator to final all real zeros to as b. _______________________________
many decimal places as the calculator will give.
10. Explain why the polynomial function defined by 10. ________________________________
( )
42
2 7 12f x x x= + +
has no real zero.
11. Graph the functions defined by
( )
3
1
f x x=
and
( ) ( )
3
22 3 1f x x= − +
on the same axes. Explain how
the graph of
2
f
can be obtained by a translation of the
graph of
1.f
11.
________________________________
________________________________
83
CHAPTER 3, FORM D
12. Use end behavior to determine which of the following graphs 12. _______________________________
is that of
( )
84
4 3.f x x x x= + − +
a. b.
c. d.
Graph each polynomial function. Factor first if the expression is not in factored form.
13.
( ) ( ) ( ) ( )
3 1 1 2f x x x x x= − − −
13. _______________________________
14.
( ) ( ) ( ) ( )
3 2 2f x x x x x= − − + −
14. _______________________________
15.
( )
432
2 8 8f x x x x= − −
15. _______________________________
16. Find a cubic polynomial having the graph shown. 16. _______________________________
17. A technique measuring cardiac output depends 17. _______________________________
on the concentration of a dye in the bloodstream
after a known amount is injected into a vein near
the heart. For a normal heart, the concentration of
dye in the bloodstream at time x (in seconds) is
modeled by the function
( )
4 3 2
.006 .140 .053 1.79 .g x x x x x= − + − +
According to this model, during what period of
time is the concentration increasing? (Round to
the nearest tenth of a second.)
84
CHAPTER 3, FORM D
18.
( )
4
3
fx x
−
=+
18.
19.
( )
2
3
4
fx x
=−
19.
20. For the rational function defined by
( )
221
,
3
xx
fx x
−+
=−
a. determine the equation of the oblique asymptote; 20. a. _____________________________
b. determine the x-intercepts; b. ____________________________
c. determine the y-intercept; c. ____________________________
d. determine the equation of the vertical asymptote; d. ____________________________
e. sketch the graph. e.
85
CHAPTER 3, FORM D
21. The intensity I of light varies inversely as the 21. _______________________________
square of the distance D from the source. If the
intensity of illumination on a screen 5 ft from a
light is 2 foot candles, find the intensity on a
screen 15 ft from the light.
22. The pitch P of a musical tone varies inversely 22. _______________________________
as its wavelength W. One tone has a pitch of
382 vibrations per second and a wavelength
of 18.9 ft. Find the wavelength of another tone
that has a pitch of 474 vibrations per second.
86
CHAPTER 3, FORM E
COLLEGE ALGEBRA
NAME
DATE
Choose the best answer.
1. Give the axis and vertex of the graph of 1. ______________
( ) ( )
2
4 10.f x x= + +
a. Axis:
4;x=−
vertex:
()
4, 10−−
b. Axis:
4;x=−
vertex:
()
4,10−
c. Axis:
4;x=
vertex:
()
4,10
d. Axis:
4;x=
vertex:
()
4,10−
2. A ball is thrown downward from a window in a tall building. 2. ______________
Its position at time t in sections is
2
16 32 ,s t t=+
where
s is in feet. How long (to the nearest tenth) will it take the ball
to fall 90 feet?
a. 1.6 sec b. 1.8 sec
c. 2.4 sec d. 2.6 sec
3. Use synthetic division to perform the division. 3. ______________
32
7
2
xx
x
−+
+
a.
25
36 2
xx x
+ + + +
b.
25
36 2
xx x
− + − +
c.
26
36 2
xx x
− + + +
d.
26
2 66 2
xx x
− + + +
4. Use synthetic division to determine
( )
2,f−
if 4. ______________
( )
32
4 3 5 9.f x x x x= − − +
a.
39−
b. 19 c.
25−
d.
46−
5. Which of the following is a factor of
32
9 2 10?x x x− + + −
5. ______________
a.
10x+
b.
10x−
c.
1x+
d.
1x−
6. Use synthetic division to determine the remainder r:
32
7 3 5 1
1
x x x
x
− − +
+
6. ______________
a.
4−
b. 2 c. 4 d. 10
7. Find all rational zeros of the function
( ) ( ) ( )
2 6 11 .f x x x x= − +
7. ______________
a. 0,6,11 b.
11,6,11−
c.
11, 6,0−−
d.
11,0, 6−
87
CHAPTER 3, FORM E
8.
( )
fx
is a third degree polynomial having only real coefficients. 8. ______________
It has 3, i, and
i−
as zeros, and the point (2, 25) lies on the graph.
Find
( )
.fx
a.
( )
32
33f x x x x= − + −
b.
( )
32
5 15 5 15f x x x x= − + − +
c.
( )
32
5 15 5 15f x x x x= − + + −
d.
( )
32
5 15 5 15f x x x x= − − +
9. Show that the polynomial function
( )
4
5 10 12f x x x= − −
9. ______________
has no real zero greater than 2.
a. When
( )
fx
is divided by
2,x−
the alternating signs in
the bottom row indicate an upper bound.
b. When
( )
fx
is divided by
2,x+
the alternating signs in
the bottom row indicate an upper bound.
c. When
( )
fx
is divided by
2,x+
the bottom row with all
signs nonnegative indicates an upper bound.
d. When
( )
fx
is divided by
2,x−
the bottom row with all
signs nonnegative indicates an upper bound.
10. Consider the function defined by
( )
32
7 2 3 10.f x x x x= + − +
10. ______________
Use the intermediate value theorem to find two consecutive
integers between with f has a zero.
a.
1, 0−
b.
2, 1−−
c.
0,1
d.
1, 2
11. The functions
( ) ( )
3
11f x x=+
and
( ) ( )
3
242f x x= − +
are 11. ______________
graphed on the same axes. Explain how the graph of
2
f
can
be obtained by a translation of the graph of
1.f
a. Shift the graph 6 units left and 2 units up.
b. Shift the graph 6 units right and 2 units down.
c. Shift the graph 5 units right and 2 units down.
d. Shift the graph 5 units left and 2 units up.
88
CHAPTER 3, FORM E
12. Use end behavior to determine which of the following graphs 12. ______________
is that of
( )
42
5 10.f x x x= − −
a. b.
c. d.
Graph each polynomial function.
13.
( )
( 3)( 2)( 2)f x x x x x= − + −
13. ______________
a. b.
c. d.
89
CHAPTER 3, FORM E
14. Factor
( )
32
2 36 72f x x x x= − − +
given that 6 is a zero of
( )
.fx
14. ______________
a.
( )
( 2)( 6)f x x x x= − +
b.
( )
( 6)( 2)( 6)f x x x x= − − +
c.
( )
( 6)( 2)( 2)f x x x x= − − +
d.
( )
( 6)( 2)( 6)f x x x x= − + +
15. Use a graphing calculator to find a real zero that is 15. ______________
approximate to the nearest tenth for this polynomial.
( )
32f x x x= − +
a. 2.1 b. 1.9
c.
1.5−
d. No real zeros
16. Find a cubic polynomial having the graph shown. 16. ______________
a.
( )
32
2f x x x x= − + +
b.
( )
32
2f x x x x= − −
c.
( )
32
2 2 4f x x x x= − −
d.
( )
32
2 2 4f x x x x= − + +
17. Which one of the functions defined below has a graph 17. ______________
with no x–intercepts?
a.
( )
1
2
fx x
=−
b.
( )
1
3
x
fx x
+
=−
c.
( )
1
x
fx x
=−
d.
( )
2
2 8 3f x x x= − − −
90
CHAPTER 3, FORM E
Graph each rational function.
18.
( )
2
1
fx x
=−
18. ______________
a. b.
c. d.
19.
( )
2
4
2
x
fx x
−
=+
19. ______________
a. b.
c. d.
91
CHAPTER 3, FORM E
20. For the rational function defined by
( )
279
,
4
xx
fx x
−−
=−
20. ______________
determine the equation of the oblique asymptote.
a.
3yx=+
b.
3yx=−
c.
11yx=+
d.
11yx=−
21. For a fixed period of time, the amount of interest varies jointly 21. ______________
as the principal and the interest rate. If a principal of $2000
invested at a rate of 6% earns $300 in interest, how much
interest will a principal of $4000 earn if it is invested at 8%?
a. $8000 b. $800
c. $80 d. $1600
22. The speed of a gear varies directly as the number of teeth it 22. ______________
contains. If a gear with 10 teeth rotates at 240 rpm, with what
speed would a gear with 18 teeth revolve under the same
conditions?
a. 432 rpm b. 480 rpm
c. 133 rpm d. 672 rpm
92
CHAPTER 3, FORM F
COLLEGE ALGEBRA
NAME
DATE
Choose the best answer.
1. Give the axis and vertex of the graph of
( )
2
4 16 19.f x x x= − +
1. ______________
a. Axis:
2;x=
vertex:
( )
2.3
b. Axis:
2;x=
vertex:
()
2, 3−
c. Axis:
1;
2
x=
vertex:
1,3
2
d. Axis:
1;
2
x=
vertex:
1,3
2
−
2. The height in feet of an object thrown upward is given 2. ______________
by the equation
2
48 16 ,h t t=−
where h is the height of the
object after t seconds. Find the maximum height the object
reaches.
a.
3
2
ft b. 28 ft
c. 36 ft d. 144 ft
3. Use synthetic division to determine
( )
4,f−
if 3. ______________
32
6 2 5 10
2
x x x
x
− + + −
−
a.
225
6 10 15 2
xx x
− − − − −
b.
240
6 10 15 2
xx x
− − − − −
c.
240
6 10 25 2
xx x
− − − − −
d.
210
6 10 5 2
xxx
− − − − −
4. Use synthetic division to determine
( )
4,f−
if 4. ______________
( )
32
4 12 8 25.f x x x x= + − +
a. 7 b. 3 c.
1−
d.
7−
5. Which of the following is a factor of 5. ______________
32
5 9 219?x x x− + +
a.
3x+
b.
73x+
c.
73x−
d.
3x−
6. Use synthetic division to determine the remainder r:
32
2 3 18 4
2
x x x
x
+ − −
−
6. ______________
a. 0 b. 7 c.
12−
d.
14−
7. Find all rational zeros of the function
( )
32
4 12 3.f x x x x= − − +
7. ______________
a.
11
, ,3
22
−
b.
3, 2,3−−
c.
13
, ,3
22
−
d.
5
1, 2, 2
93
CHAPTER 3, FORM F
8.
( )
fx
is a fourth degree polynomial having only real coefficients. 8. ______________
It has
1,−
3, and
i
as zeros, and the point (2,
30−
) lies on the graph.
Find
( )
.fx
a.
( )
432
2 2 2 3f x x x x x= − − − −
b.
( )
42
53f x x x x= − − −
c.
( )
432
2 4 4 4 6f x x x x x= − − − −
d.
( )
432
2 4 2 4 6f x x x x x= + − + −
9. Show that the polynomial function
( )
32
2 7 4 1f x x x x= − + +
9. ______________
has no real zero greater than
2.−
a. When
( )
fx
is divided by
2,x+
the alternating signs in
the bottom row indicate a lower bound.
b. When
( )
fx
is divided by
2,x−
the alternating signs in
the bottom row indicate a lower bound.
c. When
( )
fx
is divided by
2,x+
the bottom row with all
signs nonnegative indicates a lower bound.
d. When
( )
fx
is divided by
2,x−
the bottom row with all
signs nonnegative indicates a lower bound.
10. Consider the function defined by 10. ______________
( )
43
8 4 5 9.f x x x x= − − −
Use the intermediate value theorem to find two consecutive
integers between with f has a zero.
a.
1, 0−
b.
2,3
c.
0,1
d.
3, 4
11. The functions
( ) ( )
4
123f x x= − −
and
( ) ( )
4
22 1 5f x x= − + −
are 11. ______________
graphed on the same axes. Explain how the graph of
2
f
can
be obtained by a translation of the graph of
1.f
a. Shift the graph 1 unit left and 5 units down.
b. Shift the graph 1 unit right and 5 units up.
c. Shift the graph 4 units right and 5 units down.
d. Shift the graph 4 units left and 5 units down.
94
CHAPTER 3, FORM F
12. Use end behavior to determine which of the following graphs 12. ______________
is that of
( )
32
3 1.f x x x x= − + +
a. b.
c. d.
Graph each polynomial function.
13.
( )
( 3)( 2)( 2)f x x x x x= − + −
13. ______________
a. b.
c. d.
95
CHAPTER 3, FORM F
14. Factor
( )
32
2 3 5 6f x x x x= − − +
given that 1 is a zero of
( )
.fx
14. ______________
a.
( )
( 1)( 1)(3 2)f x x x x= − + −
b.
( )
( 1)( 2)(2 3)f x x x x= + + +
c.
( )
( 1)( 2)(2 3)f x x x x= − − +
d.
( )
( 1)( 2)( 2)f x x x x= − + −
15. Use a graphing calculator to find a real zero that is 15. ______________
approximate to the nearest tenth for this polynomial.
( )
4 3 2
3 3 4 4f x x x x x= + − − −
a.
1.2−
b.
.7−
c. .2 d. No real zeros
16. Find a cubic polynomial having the graph shown. 16. ______________
a.
( )
32
11
22
f x x x x= − −
b.
( )
32
2f x x x x= − + +
c.
( )
32
2f x x x x= − −
d.
( )
32
11
22
f x x x x= − + +
96
CHAPTER 3, FORM F
17. Which one of the functions defined below has a graph with no y-intercept? 17. ______________
a.
( )
2
2
3x
fx x
−
=
b.
( )
3
2
x
fx x
+
=−
c.
( )
2
23
x
fx x
=−
d.
( )
2
3
fx x
=−
Graph each rational function.
18.
( )
3
2
fx x
−
=+
18. ______________
a. b.
c. d.
97
CHAPTER 3, FORM F
19.
( )
2
4
4
fx x
−
=−
19. ______________
a. b.
c. d.
20. For the rational function defined by
( )
2
2 3 5 ,
xx
fx x
+−
=
20. ______________
determine the equation of the oblique asymptote.
a.
23yx=−
b.
23yx=+
c.
34yx=+
d.
35yx=+
21. The time it takes to complete a certain job varies inversely to the 21. ______________
number of people working on that job. If it takes 32 hours for 7
carpenters to frame a house, then how long will it take 56 carpenters
to do the job?
a. 4 hours b. 12.3 hours
c. 40 hours d. 56 hours
22. For a fixed interest rate, interest varies jointly as the principal 22. ______________
and the time in years. If a principal of $5000 invested for 4 yr
earns $900, how much will $6000 invested for 3 yr earn at the
same interest rate?
a. $180 b. $810
c. $900 d. $1800
98
CHAPTER 3, FORM A
99
100
101
CHAPTER 3, FORM B
102
103
104
CHAPTER 3, FORM C
105
106
107
CHAPTER 3, FORM D
109
110
CHAPTER 3, FORM E
111
CHAPTER 3, FORM F